I been thinking about this with sizing battery storage, on the coldest 20 days (for example) any DHW heating in the daytime will be at high rate as any reasonable sized battery will not cover all daytime usage of a heatpump. Heating DHW when PV is generating can lose 15p per kwh in export payments. Battery power will cost me about 20% over cheaprate due to loses from charge/discharge.
Unless heatpump oversized, heating DHW with heatpump on the coldest days will likely reduce COP for heating as a higher flow temperature will be required to recover the house temperature. But this will not show up in the DHW COP.
I was expecting more difference between 1pm and 1am. It looks like even with unlimited battery capacity the loses from charger/inverter will be more then the gain from heating DWH in afternoon.
When on cheap overnight rate and doing two reheats a day, why not set the overnight reheat to a higher target temperature so the daytime reheat is shorter? Both daytime COP and nighttime COP would be lower, but economics and carbon intensity should be better.
Overnight is likely to be far colder temps than day, its why the cosy tariff low period just before peak is so attractive, because its not in the cold of night.
That very sensitive to battery size, as Octopus IO lets you fill a battery cheaper but only once a day. If choosing a battery I rather have a large B gade DIY assembled battery (eg Fogstar) that will cover all daytime usage most then a small well know brand that I need to cycles each day.